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Diffstat (limited to 'sysdeps/ia64/fpu/s_log1pl.S')
| -rw-r--r-- | sysdeps/ia64/fpu/s_log1pl.S | 1200 |
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diff --git a/sysdeps/ia64/fpu/s_log1pl.S b/sysdeps/ia64/fpu/s_log1pl.S deleted file mode 100644 index 9654265004..0000000000 --- a/sysdeps/ia64/fpu/s_log1pl.S +++ /dev/null @@ -1,1200 +0,0 @@ -.file "log1pl.s" - - -// Copyright (c) 2000 - 2003, Intel Corporation -// All rights reserved. -// -// Contributed 2000 by the Intel Numerics Group, Intel Corporation -// -// Redistribution and use in source and binary forms, with or without -// modification, are permitted provided that the following conditions are -// met: -// -// * Redistributions of source code must retain the above copyright -// notice, this list of conditions and the following disclaimer. -// -// * Redistributions in binary form must reproduce the above copyright -// notice, this list of conditions and the following disclaimer in the -// documentation and/or other materials provided with the distribution. -// -// * The name of Intel Corporation may not be used to endorse or promote -// products derived from this software without specific prior written -// permission. - -// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS -// "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT -// LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR -// A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL INTEL OR ITS -// CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, -// EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, -// PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR -// PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY -// OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY OR TORT (INCLUDING -// NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS -// SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. -// -// Intel Corporation is the author of this code, and requests that all -// problem reports or change requests be submitted to it directly at -// http://www.intel.com/software/products/opensource/libraries/num.htm. -// -//********************************************************************* -// -// History: -// 02/02/00 Initial version -// 04/04/00 Unwind support added -// 08/15/00 Bundle added after call to __libm_error_support to properly -// set [the previously overwritten] GR_Parameter_RESULT. -// 05/21/01 Removed logl and log10l, putting them in a separate file -// 06/29/01 Improved speed of all paths -// 05/20/02 Cleaned up namespace and sf0 syntax -// 02/10/03 Reordered header: .section, .global, .proc, .align; -// used data8 for long double table values -// -//********************************************************************* -// -//********************************************************************* -// -// Function: log1pl(x) = ln(x+1), for double-extended precision x values -// -//********************************************************************* -// -// Resources Used: -// -// Floating-Point Registers: f8 (Input and Return Value) -// f34-f82 -// -// General Purpose Registers: -// r32-r56 -// r53-r56 (Used to pass arguments to error handling routine) -// -// Predicate Registers: p6-p13 -// -//********************************************************************* -// -// IEEE Special Conditions: -// -// Denormal fault raised on denormal inputs -// Overflow exceptions cannot occur -// Underflow exceptions raised when appropriate for log1p -// Inexact raised when appropriate by algorithm -// -// log1pl(inf) = inf -// log1pl(-inf) = QNaN -// log1pl(+/-0) = +/-0 -// log1pl(-1) = -inf -// log1pl(SNaN) = QNaN -// log1pl(QNaN) = QNaN -// log1pl(EM_special Values) = QNaN -// -//********************************************************************* -// -// Overview -// -// The method consists of three cases. -// -// If |X| < 2^(-80) use case log1p_small; -// else |X| < 2^(-7) use case log_near1; -// else use case log_regular; -// -// Case log1p_small: -// -// log1pl( X ) = logl( X+1 ) can be approximated by X -// -// Case log_near1: -// -// log1pl( X ) = log( X+1 ) can be approximated by a simple polynomial -// in W = X. This polynomial resembles the truncated Taylor -// series W - W^/2 + W^3/3 - ... -// -// Case log_regular: -// -// Here we use a table lookup method. The basic idea is that in -// order to compute logl(Arg) = log1pl (Arg-1) for an argument Arg in [1,2), -// we construct a value G such that G*Arg is close to 1 and that -// logl(1/G) is obtainable easily from a table of values calculated -// beforehand. Thus -// -// logl(Arg) = logl(1/G) + logl(G*Arg) -// = logl(1/G) + logl(1 + (G*Arg - 1)) -// -// Because |G*Arg - 1| is small, the second term on the right hand -// side can be approximated by a short polynomial. We elaborate -// this method in four steps. -// -// Step 0: Initialization -// -// We need to calculate logl( X+1 ). Obtain N, S_hi such that -// -// X+1 = 2^N * ( S_hi + S_lo ) exactly -// -// where S_hi in [1,2) and S_lo is a correction to S_hi in the sense -// that |S_lo| <= ulp(S_hi). -// -// Step 1: Argument Reduction -// -// Based on S_hi, obtain G_1, G_2, G_3 from a table and calculate -// -// G := G_1 * G_2 * G_3 -// r := (G * S_hi - 1) + G * S_lo -// -// These G_j's have the property that the product is exactly -// representable and that |r| < 2^(-12) as a result. -// -// Step 2: Approximation -// -// -// logl(1 + r) is approximated by a short polynomial poly(r). -// -// Step 3: Reconstruction -// -// -// Finally, log1pl( X ) = logl( X+1 ) is given by -// -// logl( X+1 ) = logl( 2^N * (S_hi + S_lo) ) -// ~=~ N*logl(2) + logl(1/G) + logl(1 + r) -// ~=~ N*logl(2) + logl(1/G) + poly(r). -// -// **** Algorithm **** -// -// Case log1p_small: -// -// Although log1pl(X) is basically X, we would like to preserve the inexactness -// nature as well as consistent behavior under different rounding modes. -// We can do this by computing the result as -// -// log1pl(X) = X - X*X -// -// -// Case log_near1: -// -// Here we compute a simple polynomial. To exploit parallelism, we split -// the polynomial into two portions. -// -// W := X -// Wsq := W * W -// W4 := Wsq*Wsq -// W6 := W4*Wsq -// Y_hi := W + Wsq*(P_1 + W*(P_2 + W*(P_3 + W*P_4)) -// Y_lo := W6*(P_5 + W*(P_6 + W*(P_7 + W*P_8))) -// -// Case log_regular: -// -// We present the algorithm in four steps. -// -// Step 0. Initialization -// ---------------------- -// -// Z := X + 1 -// N := unbaised exponent of Z -// S_hi := 2^(-N) * Z -// S_lo := 2^(-N) * { (max(X,1)-Z) + min(X,1) } -// -// Step 1. Argument Reduction -// -------------------------- -// -// Let -// -// Z = 2^N * S_hi = 2^N * 1.d_1 d_2 d_3 ... d_63 -// -// We obtain G_1, G_2, G_3 by the following steps. -// -// -// Define X_0 := 1.d_1 d_2 ... d_14. This is extracted -// from S_hi. -// -// Define A_1 := 1.d_1 d_2 d_3 d_4. This is X_0 truncated -// to lsb = 2^(-4). -// -// Define index_1 := [ d_1 d_2 d_3 d_4 ]. -// -// Fetch Z_1 := (1/A_1) rounded UP in fixed point with -// fixed point lsb = 2^(-15). -// Z_1 looks like z_0.z_1 z_2 ... z_15 -// Note that the fetching is done using index_1. -// A_1 is actually not needed in the implementation -// and is used here only to explain how is the value -// Z_1 defined. -// -// Fetch G_1 := (1/A_1) truncated to 21 sig. bits. -// floating pt. Again, fetching is done using index_1. A_1 -// explains how G_1 is defined. -// -// Calculate X_1 := X_0 * Z_1 truncated to lsb = 2^(-14) -// = 1.0 0 0 0 d_5 ... d_14 -// This is accomplised by integer multiplication. -// It is proved that X_1 indeed always begin -// with 1.0000 in fixed point. -// -// -// Define A_2 := 1.0 0 0 0 d_5 d_6 d_7 d_8. This is X_1 -// truncated to lsb = 2^(-8). Similar to A_1, -// A_2 is not needed in actual implementation. It -// helps explain how some of the values are defined. -// -// Define index_2 := [ d_5 d_6 d_7 d_8 ]. -// -// Fetch Z_2 := (1/A_2) rounded UP in fixed point with -// fixed point lsb = 2^(-15). Fetch done using index_2. -// Z_2 looks like z_0.z_1 z_2 ... z_15 -// -// Fetch G_2 := (1/A_2) truncated to 21 sig. bits. -// floating pt. -// -// Calculate X_2 := X_1 * Z_2 truncated to lsb = 2^(-14) -// = 1.0 0 0 0 0 0 0 0 d_9 d_10 ... d_14 -// This is accomplised by integer multiplication. -// It is proved that X_2 indeed always begin -// with 1.00000000 in fixed point. -// -// -// Define A_3 := 1.0 0 0 0 0 0 0 0 d_9 d_10 d_11 d_12 d_13 1. -// This is 2^(-14) + X_2 truncated to lsb = 2^(-13). -// -// Define index_3 := [ d_9 d_10 d_11 d_12 d_13 ]. -// -// Fetch G_3 := (1/A_3) truncated to 21 sig. bits. -// floating pt. Fetch is done using index_3. -// -// Compute G := G_1 * G_2 * G_3. -// -// This is done exactly since each of G_j only has 21 sig. bits. -// -// Compute -// -// r := (G*S_hi - 1) + G*S_lo using 2 FMA operations. -// -// Thus r approximates G*(S_hi + S_lo) - 1 to within a couple of -// rounding errors. -// -// -// Step 2. Approximation -// --------------------- -// -// This step computes an approximation to logl( 1 + r ) where r is the -// reduced argument just obtained. It is proved that |r| <= 1.9*2^(-13); -// thus logl(1+r) can be approximated by a short polynomial: -// -// logl(1+r) ~=~ poly = r + Q1 r^2 + ... + Q4 r^5 -// -// -// Step 3. Reconstruction -// ---------------------- -// -// This step computes the desired result of logl(X+1): -// -// logl(X+1) = logl( 2^N * (S_hi + S_lo) ) -// = N*logl(2) + logl( S_hi + S_lo) ) -// = N*logl(2) + logl(1/G) + -// logl(1 + G * ( S_hi + S_lo ) - 1 ) -// -// logl(2), logl(1/G_j) are stored as pairs of (single,double) numbers: -// log2_hi, log2_lo, log1byGj_hi, log1byGj_lo. The high parts are -// single-precision numbers and the low parts are double precision -// numbers. These have the property that -// -// N*log2_hi + SUM ( log1byGj_hi ) -// -// is computable exactly in double-extended precision (64 sig. bits). -// Finally -// -// Y_hi := N*log2_hi + SUM ( log1byGj_hi ) -// Y_lo := poly_hi + [ poly_lo + -// ( SUM ( log1byGj_lo ) + N*log2_lo ) ] -// - -RODATA -.align 64 - -// ************* DO NOT CHANGE THE ORDER OF THESE TABLES ************* - -// P_8, P_7, P_6, P_5, P_4, P_3, P_2, and P_1 - -LOCAL_OBJECT_START(Constants_P) -//data4 0xEFD62B15,0xE3936754,0x00003FFB,0x00000000 -//data4 0xA5E56381,0x8003B271,0x0000BFFC,0x00000000 -//data4 0x73282DB0,0x9249248C,0x00003FFC,0x00000000 -//data4 0x47305052,0xAAAAAA9F,0x0000BFFC,0x00000000 -//data4 0xCCD17FC9,0xCCCCCCCC,0x00003FFC,0x00000000 -//data4 0x00067ED5,0x80000000,0x0000BFFD,0x00000000 -//data4 0xAAAAAAAA,0xAAAAAAAA,0x00003FFD,0x00000000 -//data4 0xFFFFFFFE,0xFFFFFFFF,0x0000BFFD,0x00000000 -data8 0xE3936754EFD62B15,0x00003FFB -data8 0x8003B271A5E56381,0x0000BFFC -data8 0x9249248C73282DB0,0x00003FFC -data8 0xAAAAAA9F47305052,0x0000BFFC -data8 0xCCCCCCCCCCD17FC9,0x00003FFC -data8 0x8000000000067ED5,0x0000BFFD -data8 0xAAAAAAAAAAAAAAAA,0x00003FFD -data8 0xFFFFFFFFFFFFFFFE,0x0000BFFD -LOCAL_OBJECT_END(Constants_P) - -// log2_hi, log2_lo, Q_4, Q_3, Q_2, and Q_1 - -LOCAL_OBJECT_START(Constants_Q) -//data4 0x00000000,0xB1721800,0x00003FFE,0x00000000 -//data4 0x4361C4C6,0x82E30865,0x0000BFE2,0x00000000 -//data4 0x328833CB,0xCCCCCAF2,0x00003FFC,0x00000000 -//data4 0xA9D4BAFB,0x80000077,0x0000BFFD,0x00000000 -//data4 0xAAABE3D2,0xAAAAAAAA,0x00003FFD,0x00000000 -//data4 0xFFFFDAB7,0xFFFFFFFF,0x0000BFFD,0x00000000 -data8 0xB172180000000000,0x00003FFE -data8 0x82E308654361C4C6,0x0000BFE2 -data8 0xCCCCCAF2328833CB,0x00003FFC -data8 0x80000077A9D4BAFB,0x0000BFFD -data8 0xAAAAAAAAAAABE3D2,0x00003FFD -data8 0xFFFFFFFFFFFFDAB7,0x0000BFFD -LOCAL_OBJECT_END(Constants_Q) - -// 1/ln10_hi, 1/ln10_lo - -LOCAL_OBJECT_START(Constants_1_by_LN10) -//data4 0x37287195,0xDE5BD8A9,0x00003FFD,0x00000000 -//data4 0xACCF70C8,0xD56EAABE,0x00003FBB,0x00000000 -data8 0xDE5BD8A937287195,0x00003FFD -data8 0xD56EAABEACCF70C8,0x00003FBB -LOCAL_OBJECT_END(Constants_1_by_LN10) - - -// Z1 - 16 bit fixed - -LOCAL_OBJECT_START(Constants_Z_1) -data4 0x00008000 -data4 0x00007879 -data4 0x000071C8 -data4 0x00006BCB -data4 0x00006667 -data4 0x00006187 -data4 0x00005D18 -data4 0x0000590C -data4 0x00005556 -data4 0x000051EC -data4 0x00004EC5 -data4 0x00004BDB -data4 0x00004925 -data4 0x0000469F -data4 0x00004445 -data4 0x00004211 -LOCAL_OBJECT_END(Constants_Z_1) - -// G1 and H1 - IEEE single and h1 - IEEE double - -LOCAL_OBJECT_START(Constants_G_H_h1) -data4 0x3F800000,0x00000000 -data8 0x0000000000000000 -data4 0x3F70F0F0,0x3D785196 -data8 0x3DA163A6617D741C -data4 0x3F638E38,0x3DF13843 -data8 0x3E2C55E6CBD3D5BB -data4 0x3F579430,0x3E2FF9A0 -data8 0xBE3EB0BFD86EA5E7 -data4 0x3F4CCCC8,0x3E647FD6 -data8 0x3E2E6A8C86B12760 -data4 0x3F430C30,0x3E8B3AE7 -data8 0x3E47574C5C0739BA -data4 0x3F3A2E88,0x3EA30C68 -data8 0x3E20E30F13E8AF2F -data4 0x3F321640,0x3EB9CEC8 -data8 0xBE42885BF2C630BD -data4 0x3F2AAAA8,0x3ECF9927 -data8 0x3E497F3497E577C6 -data4 0x3F23D708,0x3EE47FC5 -data8 0x3E3E6A6EA6B0A5AB -data4 0x3F1D89D8,0x3EF8947D -data8 0xBDF43E3CD328D9BE -data4 0x3F17B420,0x3F05F3A1 -data8 0x3E4094C30ADB090A -data4 0x3F124920,0x3F0F4303 -data8 0xBE28FBB2FC1FE510 -data4 0x3F0D3DC8,0x3F183EBF -data8 0x3E3A789510FDE3FA -data4 0x3F088888,0x3F20EC80 -data8 0x3E508CE57CC8C98F -data4 0x3F042108,0x3F29516A -data8 0xBE534874A223106C -LOCAL_OBJECT_END(Constants_G_H_h1) - -// Z2 - 16 bit fixed - -LOCAL_OBJECT_START(Constants_Z_2) -data4 0x00008000 -data4 0x00007F81 -data4 0x00007F02 -data4 0x00007E85 -data4 0x00007E08 -data4 0x00007D8D -data4 0x00007D12 -data4 0x00007C98 -data4 0x00007C20 -data4 0x00007BA8 -data4 0x00007B31 -data4 0x00007ABB -data4 0x00007A45 -data4 0x000079D1 -data4 0x0000795D -data4 0x000078EB -LOCAL_OBJECT_END(Constants_Z_2) - -// G2 and H2 - IEEE single and h2 - IEEE double - -LOCAL_OBJECT_START(Constants_G_H_h2) -data4 0x3F800000,0x00000000 -data8 0x0000000000000000 -data4 0x3F7F00F8,0x3B7F875D -data8 0x3DB5A11622C42273 -data4 0x3F7E03F8,0x3BFF015B -data8 0x3DE620CF21F86ED3 -data4 0x3F7D08E0,0x3C3EE393 -data8 0xBDAFA07E484F34ED -data4 0x3F7C0FC0,0x3C7E0586 -data8 0xBDFE07F03860BCF6 -data4 0x3F7B1880,0x3C9E75D2 -data8 0x3DEA370FA78093D6 -data4 0x3F7A2328,0x3CBDC97A -data8 0x3DFF579172A753D0 -data4 0x3F792FB0,0x3CDCFE47 -data8 0x3DFEBE6CA7EF896B -data4 0x3F783E08,0x3CFC15D0 -data8 0x3E0CF156409ECB43 -data4 0x3F774E38,0x3D0D874D -data8 0xBE0B6F97FFEF71DF -data4 0x3F766038,0x3D1CF49B -data8 0xBE0804835D59EEE8 -data4 0x3F757400,0x3D2C531D -data8 0x3E1F91E9A9192A74 -data4 0x3F748988,0x3D3BA322 -data8 0xBE139A06BF72A8CD -data4 0x3F73A0D0,0x3D4AE46F -data8 0x3E1D9202F8FBA6CF -data4 0x3F72B9D0,0x3D5A1756 -data8 0xBE1DCCC4BA796223 -data4 0x3F71D488,0x3D693B9D -data8 0xBE049391B6B7C239 -LOCAL_OBJECT_END(Constants_G_H_h2) - -// G3 and H3 - IEEE single and h3 - IEEE double - -LOCAL_OBJECT_START(Constants_G_H_h3) -data4 0x3F7FFC00,0x38800100 -data8 0x3D355595562224CD -data4 0x3F7FF400,0x39400480 -data8 0x3D8200A206136FF6 -data4 0x3F7FEC00,0x39A00640 -data8 0x3DA4D68DE8DE9AF0 -data4 0x3F7FE400,0x39E00C41 -data8 0xBD8B4291B10238DC -data4 0x3F7FDC00,0x3A100A21 -data8 0xBD89CCB83B1952CA -data4 0x3F7FD400,0x3A300F22 -data8 0xBDB107071DC46826 -data4 0x3F7FCC08,0x3A4FF51C -data8 0x3DB6FCB9F43307DB -data4 0x3F7FC408,0x3A6FFC1D -data8 0xBD9B7C4762DC7872 -data4 0x3F7FBC10,0x3A87F20B -data8 0xBDC3725E3F89154A -data4 0x3F7FB410,0x3A97F68B -data8 0xBD93519D62B9D392 -data4 0x3F7FAC18,0x3AA7EB86 -data8 0x3DC184410F21BD9D -data4 0x3F7FA420,0x3AB7E101 -data8 0xBDA64B952245E0A6 -data4 0x3F7F9C20,0x3AC7E701 -data8 0x3DB4B0ECAABB34B8 -data4 0x3F7F9428,0x3AD7DD7B -data8 0x3D9923376DC40A7E -data4 0x3F7F8C30,0x3AE7D474 -data8 0x3DC6E17B4F2083D3 -data4 0x3F7F8438,0x3AF7CBED -data8 0x3DAE314B811D4394 -data4 0x3F7F7C40,0x3B03E1F3 -data8 0xBDD46F21B08F2DB1 -data4 0x3F7F7448,0x3B0BDE2F -data8 0xBDDC30A46D34522B -data4 0x3F7F6C50,0x3B13DAAA -data8 0x3DCB0070B1F473DB -data4 0x3F7F6458,0x3B1BD766 -data8 0xBDD65DDC6AD282FD -data4 0x3F7F5C68,0x3B23CC5C -data8 0xBDCDAB83F153761A -data4 0x3F7F5470,0x3B2BC997 -data8 0xBDDADA40341D0F8F -data4 0x3F7F4C78,0x3B33C711 -data8 0x3DCD1BD7EBC394E8 -data4 0x3F7F4488,0x3B3BBCC6 -data8 0xBDC3532B52E3E695 -data4 0x3F7F3C90,0x3B43BAC0 -data8 0xBDA3961EE846B3DE -data4 0x3F7F34A0,0x3B4BB0F4 -data8 0xBDDADF06785778D4 -data4 0x3F7F2CA8,0x3B53AF6D -data8 0x3DCC3ED1E55CE212 -data4 0x3F7F24B8,0x3B5BA620 -data8 0xBDBA31039E382C15 -data4 0x3F7F1CC8,0x3B639D12 -data8 0x3D635A0B5C5AF197 -data4 0x3F7F14D8,0x3B6B9444 -data8 0xBDDCCB1971D34EFC -data4 0x3F7F0CE0,0x3B7393BC -data8 0x3DC7450252CD7ADA -data4 0x3F7F04F0,0x3B7B8B6D -data8 0xBDB68F177D7F2A42 -LOCAL_OBJECT_END(Constants_G_H_h3) - - -// Floating Point Registers - -FR_Input_X = f8 - -FR_Y_hi = f34 -FR_Y_lo = f35 - -FR_Scale = f36 -FR_X_Prime = f37 -FR_S_hi = f38 -FR_W = f39 -FR_G = f40 - -FR_H = f41 -FR_wsq = f42 -FR_w4 = f43 -FR_h = f44 -FR_w6 = f45 - -FR_G2 = f46 -FR_H2 = f47 -FR_poly_lo = f48 -FR_P8 = f49 -FR_poly_hi = f50 - -FR_P7 = f51 -FR_h2 = f52 -FR_rsq = f53 -FR_P6 = f54 -FR_r = f55 - -FR_log2_hi = f56 -FR_log2_lo = f57 -FR_p87 = f58 -FR_p876 = f58 -FR_p8765 = f58 -FR_float_N = f59 -FR_Q4 = f60 - -FR_p43 = f61 -FR_p432 = f61 -FR_p4321 = f61 -FR_P4 = f62 -FR_G3 = f63 -FR_H3 = f64 -FR_h3 = f65 - -FR_Q3 = f66 -FR_P3 = f67 -FR_Q2 = f68 -FR_P2 = f69 -FR_1LN10_hi = f70 - -FR_Q1 = f71 -FR_P1 = f72 -FR_1LN10_lo = f73 -FR_P5 = f74 -FR_rcub = f75 - -FR_Output_X_tmp = f76 -FR_Neg_One = f77 -FR_Z = f78 -FR_AA = f79 -FR_BB = f80 -FR_S_lo = f81 -FR_2_to_minus_N = f82 - -FR_X = f8 -FR_Y = f0 -FR_RESULT = f76 - - -// General Purpose Registers - -GR_ad_p = r33 -GR_Index1 = r34 -GR_Index2 = r35 -GR_signif = r36 -GR_X_0 = r37 -GR_X_1 = r38 -GR_X_2 = r39 -GR_minus_N = r39 -GR_Z_1 = r40 -GR_Z_2 = r41 -GR_N = r42 -GR_Bias = r43 -GR_M = r44 -GR_Index3 = r45 -GR_exp_2tom80 = r45 -GR_ad_p2 = r46 -GR_exp_mask = r47 -GR_exp_2tom7 = r48 -GR_ad_ln10 = r49 -GR_ad_tbl_1 = r50 -GR_ad_tbl_2 = r51 -GR_ad_tbl_3 = r52 -GR_ad_q = r53 -GR_ad_z_1 = r54 -GR_ad_z_2 = r55 -GR_ad_z_3 = r56 -GR_minus_N = r39 - -// -// Added for unwind support -// - -GR_SAVE_PFS = r50 -GR_SAVE_B0 = r51 -GR_SAVE_GP = r52 -GR_Parameter_X = r53 -GR_Parameter_Y = r54 -GR_Parameter_RESULT = r55 -GR_Parameter_TAG = r56 - -.section .text -GLOBAL_IEEE754_ENTRY(log1pl) -{ .mfi - alloc r32 = ar.pfs,0,21,4,0 - fclass.m p6, p0 = FR_Input_X, 0x1E3 // Test for natval, nan, inf - nop.i 999 -} -{ .mfi - addl GR_ad_z_1 = @ltoff(Constants_Z_1#),gp - fma.s1 FR_Z = FR_Input_X, f1, f1 // x+1 - nop.i 999 -} -;; - -{ .mfi - nop.m 999 - fmerge.ns FR_Neg_One = f1, f1 // Form -1.0 - nop.i 999 -} -{ .mfi - nop.m 999 - fnorm.s1 FR_X_Prime = FR_Input_X // Normalize x - nop.i 999 -} -;; - -{ .mfi - ld8 GR_ad_z_1 = [GR_ad_z_1] // Get pointer to Constants_Z_1 - nop.f 999 - mov GR_exp_2tom7 = 0x0fff8 // Exponent of 2^-7 -} -;; - -{ .mfb - getf.sig GR_signif = FR_Z // Get significand of x+1 - fcmp.eq.s1 p9, p0 = FR_Input_X, f0 // Test for x=0 -(p6) br.cond.spnt LOG1P_special // Branch for nan, inf, natval -} -;; - -{ .mfi - add GR_ad_tbl_1 = 0x040, GR_ad_z_1 // Point to Constants_G_H_h1 - fcmp.lt.s1 p13, p0 = FR_X_Prime, FR_Neg_One // Test for x<-1 - add GR_ad_p = -0x100, GR_ad_z_1 // Point to Constants_P -} -{ .mfi - add GR_ad_z_2 = 0x140, GR_ad_z_1 // Point to Constants_Z_2 - nop.f 999 - add GR_ad_tbl_2 = 0x180, GR_ad_z_1 // Point to Constants_G_H_h2 -} -;; - -{ .mfi - add GR_ad_q = 0x080, GR_ad_p // Point to Constants_Q - fcmp.eq.s1 p8, p0 = FR_X_Prime, FR_Neg_One // Test for x=-1 - extr.u GR_Index1 = GR_signif, 59, 4 // Get high 4 bits of signif -} -{ .mfb - add GR_ad_tbl_3 = 0x280, GR_ad_z_1 // Point to Constants_G_H_h3 - nop.f 999 -(p9) br.ret.spnt b0 // Exit if x=0, return input -} -;; - -{ .mfi - shladd GR_ad_z_1 = GR_Index1, 2, GR_ad_z_1 // Point to Z_1 - fclass.nm p10, p0 = FR_Input_X, 0x1FF // Test for unsupported - extr.u GR_X_0 = GR_signif, 49, 15 // Get high 15 bits of significand -} -{ .mfi - ldfe FR_P8 = [GR_ad_p],16 // Load P_8 for near1 path - fsub.s1 FR_W = FR_X_Prime, f0 // W = x - add GR_ad_ln10 = 0x060, GR_ad_q // Point to Constants_1_by_LN10 -} -;; - -{ .mfi - ld4 GR_Z_1 = [GR_ad_z_1] // Load Z_1 - fmax.s1 FR_AA = FR_X_Prime, f1 // For S_lo, form AA = max(X,1.0) - mov GR_exp_mask = 0x1FFFF // Create exponent mask -} -{ .mib - shladd GR_ad_tbl_1 = GR_Index1, 4, GR_ad_tbl_1 // Point to G_1 - mov GR_Bias = 0x0FFFF // Create exponent bias -(p13) br.cond.spnt LOG1P_LT_Minus_1 // Branch if x<-1 -} -;; - -{ .mfb - ldfps FR_G, FR_H = [GR_ad_tbl_1],8 // Load G_1, H_1 - fmerge.se FR_S_hi = f1,FR_Z // Form |x+1| -(p8) br.cond.spnt LOG1P_EQ_Minus_1 // Branch if x=-1 -} -;; - -{ .mmb - getf.exp GR_N = FR_Z // Get N = exponent of x+1 - ldfd FR_h = [GR_ad_tbl_1] // Load h_1 -(p10) br.cond.spnt LOG1P_unsupported // Branch for unsupported type -} -;; - -{ .mfi - ldfe FR_log2_hi = [GR_ad_q],16 // Load log2_hi - fcmp.eq.s0 p8, p0 = FR_Input_X, f0 // Dummy op to flag denormals - pmpyshr2.u GR_X_1 = GR_X_0,GR_Z_1,15 // Get bits 30-15 of X_0 * Z_1 -} -;; - -// -// For performance, don't use result of pmpyshr2.u for 4 cycles. -// -{ .mmi - ldfe FR_log2_lo = [GR_ad_q],16 // Load log2_lo - sub GR_N = GR_N, GR_Bias - mov GR_exp_2tom80 = 0x0ffaf // Exponent of 2^-80 -} -;; - -{ .mfi - ldfe FR_Q4 = [GR_ad_q],16 // Load Q4 - fms.s1 FR_S_lo = FR_AA, f1, FR_Z // Form S_lo = AA - Z - sub GR_minus_N = GR_Bias, GR_N // Form exponent of 2^(-N) -} -;; - -{ .mmf - ldfe FR_Q3 = [GR_ad_q],16 // Load Q3 - setf.sig FR_float_N = GR_N // Put integer N into rightmost significand - fmin.s1 FR_BB = FR_X_Prime, f1 // For S_lo, form BB = min(X,1.0) -} -;; - -{ .mmi - getf.exp GR_M = FR_W // Get signexp of w = x - ldfe FR_Q2 = [GR_ad_q],16 // Load Q2 - extr.u GR_Index2 = GR_X_1, 6, 4 // Extract bits 6-9 of X_1 -} -;; - -{ .mmi - ldfe FR_Q1 = [GR_ad_q] // Load Q1 - shladd GR_ad_z_2 = GR_Index2, 2, GR_ad_z_2 // Point to Z_2 - add GR_ad_p2 = 0x30,GR_ad_p // Point to P_4 -} -;; - -{ .mmi - ld4 GR_Z_2 = [GR_ad_z_2] // Load Z_2 - shladd GR_ad_tbl_2 = GR_Index2, 4, GR_ad_tbl_2 // Point to G_2 - and GR_M = GR_exp_mask, GR_M // Get exponent of w = x -} -;; - -{ .mmi - ldfps FR_G2, FR_H2 = [GR_ad_tbl_2],8 // Load G_2, H_2 - cmp.lt p8, p9 = GR_M, GR_exp_2tom7 // Test |x| < 2^-7 - cmp.lt p7, p0 = GR_M, GR_exp_2tom80 // Test |x| < 2^-80 -} -;; - -// Small path is separate code -// p7 is for the small path: |x| < 2^-80 -// near1 and regular paths are merged. -// p8 is for the near1 path: |x| < 2^-7 -// p9 is for regular path: |x| >= 2^-7 - -{ .mfi - ldfd FR_h2 = [GR_ad_tbl_2] // Load h_2 - nop.f 999 - nop.i 999 -} -{ .mfb -(p9) setf.exp FR_2_to_minus_N = GR_minus_N // Form 2^(-N) -(p7) fnma.s0 f8 = FR_X_Prime, FR_X_Prime, FR_X_Prime // Result x - x*x -(p7) br.ret.spnt b0 // Branch if |x| < 2^-80 -} -;; - -{ .mmi -(p8) ldfe FR_P7 = [GR_ad_p],16 // Load P_7 for near1 path -(p8) ldfe FR_P4 = [GR_ad_p2],16 // Load P_4 for near1 path -(p9) pmpyshr2.u GR_X_2 = GR_X_1,GR_Z_2,15 // Get bits 30-15 of X_1 * Z_2 -} -;; - -// -// For performance, don't use result of pmpyshr2.u for 4 cycles. -// -{ .mmf -(p8) ldfe FR_P6 = [GR_ad_p],16 // Load P_6 for near1 path -(p8) ldfe FR_P3 = [GR_ad_p2],16 // Load P_3 for near1 path -(p9) fma.s1 FR_S_lo = FR_S_lo, f1, FR_BB // S_lo = S_lo + BB -} -;; - -{ .mmf -(p8) ldfe FR_P5 = [GR_ad_p],16 // Load P_5 for near1 path -(p8) ldfe FR_P2 = [GR_ad_p2],16 // Load P_2 for near1 path -(p8) fmpy.s1 FR_wsq = FR_W, FR_W // wsq = w * w for near1 path -} -;; - -{ .mmi -(p8) ldfe FR_P1 = [GR_ad_p2],16 ;; // Load P_1 for near1 path - nop.m 999 -(p9) extr.u GR_Index3 = GR_X_2, 1, 5 // Extract bits 1-5 of X_2 -} -;; - -{ .mfi -(p9) shladd GR_ad_tbl_3 = GR_Index3, 4, GR_ad_tbl_3 // Point to G_3 -(p9) fcvt.xf FR_float_N = FR_float_N - nop.i 999 -} -;; - -{ .mfi -(p9) ldfps FR_G3, FR_H3 = [GR_ad_tbl_3],8 // Load G_3, H_3 - nop.f 999 - nop.i 999 -} -;; - -{ .mfi -(p9) ldfd FR_h3 = [GR_ad_tbl_3] // Load h_3 -(p9) fmpy.s1 FR_G = FR_G, FR_G2 // G = G_1 * G_2 - nop.i 999 -} -{ .mfi - nop.m 999 -(p9) fadd.s1 FR_H = FR_H, FR_H2 // H = H_1 + H_2 - nop.i 999 -} -;; - -{ .mmf - nop.m 999 - nop.m 999 -(p9) fadd.s1 FR_h = FR_h, FR_h2 // h = h_1 + h_2 -} -;; - -{ .mfi - nop.m 999 -(p8) fmpy.s1 FR_w4 = FR_wsq, FR_wsq // w4 = w^4 for near1 path - nop.i 999 -} -{ .mfi - nop.m 999 -(p8) fma.s1 FR_p87 = FR_W, FR_P8, FR_P7 // p87 = w * P8 + P7 - nop.i 999 -} -;; - -{ .mfi - nop.m 999 -(p9) fma.s1 FR_S_lo = FR_S_lo, FR_2_to_minus_N, f0 // S_lo = S_lo * 2^(-N) - nop.i 999 -} -{ .mfi - nop.m 999 -(p8) fma.s1 FR_p43 = FR_W, FR_P4, FR_P3 // p43 = w * P4 + P3 - nop.i 999 -} -;; - -{ .mfi - nop.m 999 -(p9) fmpy.s1 FR_G = FR_G, FR_G3 // G = (G_1 * G_2) * G_3 - nop.i 999 -} -{ .mfi - nop.m 999 -(p9) fadd.s1 FR_H = FR_H, FR_H3 // H = (H_1 + H_2) + H_3 - nop.i 999 -} -;; - -{ .mfi - nop.m 999 -(p9) fadd.s1 FR_h = FR_h, FR_h3 // h = (h_1 + h_2) + h_3 - nop.i 999 -} -{ .mfi - nop.m 999 -(p8) fmpy.s1 FR_w6 = FR_w4, FR_wsq // w6 = w^6 for near1 path - nop.i 999 -} -;; - -{ .mfi - nop.m 999 -(p8) fma.s1 FR_p432 = FR_W, FR_p43, FR_P2 // p432 = w * p43 + P2 - nop.i 999 -} -{ .mfi - nop.m 999 -(p8) fma.s1 FR_p876 = FR_W, FR_p87, FR_P6 // p876 = w * p87 + P6 - nop.i 999 -} -;; - -{ .mfi - nop.m 999 -(p9) fms.s1 FR_r = FR_G, FR_S_hi, f1 // r = G * S_hi - 1 - nop.i 999 -} -{ .mfi - nop.m 999 -(p9) fma.s1 FR_Y_hi = FR_float_N, FR_log2_hi, FR_H // Y_hi = N * log2_hi + H - nop.i 999 -} -;; - -{ .mfi - nop.m 999 -(p9) fma.s1 FR_h = FR_float_N, FR_log2_lo, FR_h // h = N * log2_lo + h - nop.i 999 -} -;; - -{ .mfi - nop.m 999 -(p9) fma.s1 FR_r = FR_G, FR_S_lo, FR_r // r = G * S_lo + (G * S_hi - 1) - nop.i 999 -} -;; - -{ .mfi - nop.m 999 -(p8) fma.s1 FR_p4321 = FR_W, FR_p432, FR_P1 // p4321 = w * p432 + P1 - nop.i 999 -} -{ .mfi - nop.m 999 -(p8) fma.s1 FR_p8765 = FR_W, FR_p876, FR_P5 // p8765 = w * p876 + P5 - nop.i 999 -} -;; - -{ .mfi - nop.m 999 -(p9) fma.s1 FR_poly_lo = FR_r, FR_Q4, FR_Q3 // poly_lo = r * Q4 + Q3 - nop.i 999 -} -{ .mfi - nop.m 999 -(p9) fmpy.s1 FR_rsq = FR_r, FR_r // rsq = r * r - nop.i 999 -} -;; - -{ .mfi - nop.m 999 -(p8) fma.s1 FR_Y_lo = FR_wsq, FR_p4321, f0 // Y_lo = wsq * p4321 - nop.i 999 -} -{ .mfi - nop.m 999 -(p8) fma.s1 FR_Y_hi = FR_W, f1, f0 // Y_hi = w for near1 path - nop.i 999 -} -;; - -{ .mfi - nop.m 999 -(p9) fma.s1 FR_poly_lo = FR_poly_lo, FR_r, FR_Q2 // poly_lo = poly_lo * r + Q2 - nop.i 999 -} -{ .mfi - nop.m 999 -(p9) fma.s1 FR_rcub = FR_rsq, FR_r, f0 // rcub = r^3 - nop.i 999 -} -;; - -{ .mfi - nop.m 999 -(p8) fma.s1 FR_Y_lo = FR_w6, FR_p8765,FR_Y_lo // Y_lo = w6 * p8765 + w2 * p4321 - nop.i 999 -} -;; - -{ .mfi - nop.m 999 -(p9) fma.s1 FR_poly_hi = FR_Q1, FR_rsq, FR_r // poly_hi = Q1 * rsq + r - nop.i 999 -} -;; - -{ .mfi - nop.m 999 -(p9) fma.s1 FR_poly_lo = FR_poly_lo, FR_rcub, FR_h // poly_lo = poly_lo*r^3 + h - nop.i 999 -} -;; - -{ .mfi - nop.m 999 -(p9) fadd.s1 FR_Y_lo = FR_poly_hi, FR_poly_lo // Y_lo = poly_hi + poly_lo - nop.i 999 -} -;; - -// Remainder of code is common for near1 and regular paths -{ .mfb - nop.m 999 - fadd.s0 f8 = FR_Y_lo,FR_Y_hi // Result=Y_lo+Y_hi - br.ret.sptk b0 // Common exit for 2^-80 < x < inf -} -;; - - -// Here if x=-1 -LOG1P_EQ_Minus_1: -// -// If x=-1 raise divide by zero and return -inf -// -{ .mfi - mov GR_Parameter_TAG = 138 - fsub.s1 FR_Output_X_tmp = f0, f1 - nop.i 999 -} -;; - -{ .mfb - nop.m 999 - frcpa.s0 FR_Output_X_tmp, p8 = FR_Output_X_tmp, f0 - br.cond.sptk __libm_error_region -} -;; - -LOG1P_special: -{ .mfi - nop.m 999 - fclass.m.unc p8, p0 = FR_Input_X, 0x1E1 // Test for natval, nan, +inf - nop.i 999 -} -;; - -// -// For SNaN raise invalid and return QNaN. -// For QNaN raise invalid and return QNaN. -// For +Inf return +Inf. -// -{ .mfb - nop.m 999 -(p8) fmpy.s0 f8 = FR_Input_X, f1 -(p8) br.ret.sptk b0 // Return for natval, nan, +inf -} -;; - -// -// For -Inf raise invalid and return QNaN. -// -{ .mfb - mov GR_Parameter_TAG = 139 - fmpy.s0 FR_Output_X_tmp = FR_Input_X, f0 - br.cond.sptk __libm_error_region -} -;; - - -LOG1P_unsupported: -// -// Return generated NaN or other value. -// -{ .mfb - nop.m 999 - fmpy.s0 f8 = FR_Input_X, f0 - br.ret.sptk b0 -} -;; - -// Here if -inf < x < -1 -LOG1P_LT_Minus_1: -// -// Deal with x < -1 in a special way - raise -// invalid and produce QNaN indefinite. -// -{ .mfb - mov GR_Parameter_TAG = 139 - frcpa.s0 FR_Output_X_tmp, p8 = f0, f0 - br.cond.sptk __libm_error_region -} -;; - - -GLOBAL_IEEE754_END(log1pl) - -LOCAL_LIBM_ENTRY(__libm_error_region) -.prologue -{ .mfi - add GR_Parameter_Y=-32,sp // Parameter 2 value - nop.f 0 -.save ar.pfs,GR_SAVE_PFS - mov GR_SAVE_PFS=ar.pfs // Save ar.pfs -} -{ .mfi -.fframe 64 - add sp=-64,sp // Create new stack - nop.f 0 - mov GR_SAVE_GP=gp // Save gp -};; -{ .mmi - stfe [GR_Parameter_Y] = FR_Y,16 // Save Parameter 2 on stack - add GR_Parameter_X = 16,sp // Parameter 1 address -.save b0, GR_SAVE_B0 - mov GR_SAVE_B0=b0 // Save b0 -};; -.body -{ .mib - stfe [GR_Parameter_X] = FR_X // Store Parameter 1 on stack - add GR_Parameter_RESULT = 0,GR_Parameter_Y - nop.b 0 // Parameter 3 address -} -{ .mib - stfe [GR_Parameter_Y] = FR_RESULT // Store Parameter 3 on stack - add GR_Parameter_Y = -16,GR_Parameter_Y - br.call.sptk b0=__libm_error_support# // Call error handling function -};; -{ .mmi - nop.m 999 - nop.m 999 - add GR_Parameter_RESULT = 48,sp -};; -{ .mmi - ldfe f8 = [GR_Parameter_RESULT] // Get return result off stack -.restore sp - add sp = 64,sp // Restore stack pointer - mov b0 = GR_SAVE_B0 // Restore return address -};; -{ .mib - mov gp = GR_SAVE_GP // Restore gp - mov ar.pfs = GR_SAVE_PFS // Restore ar.pfs - br.ret.sptk b0 // Return -};; - -LOCAL_LIBM_END(__libm_error_region#) - -.type __libm_error_support#,@function -.global __libm_error_support# |